function value = r8cbb_get ( n1, n2, ml, mu, a, i, j )
%*****************************************************************************80
%
%% R8CBB_GET returns the value of an entry of a R8CBB matrix.
%
% Discussion:
%
% The R8CBB storage format is for a compressed border banded matrix.
% Such a matrix has the logical form:
%
% A1 | A2
% ---+---
% A3 | A4
%
% with A1 a (usually large) N1 by N1 banded matrix, while A2, A3 and A4
% are dense rectangular matrices of orders N1 by N2, N2 by N1, and N2 by N2,
% respectively.
%
% The R8CBB format is the same as the DBB format, except that the banded
% matrix A1 is stored in compressed band form rather than standard
% banded form. In other words, we do not include the extra room
% set aside for fill in during pivoting.
%
% A should be defined as a vector. The user must then store
% the entries of the four blocks of the matrix into the vector A.
% Each block is stored by columns.
%
% A1, the banded portion of the matrix, is stored in
% the first (ML+MU+1)*N1 entries of A, using the obvious variant
% of the LINPACK general band format.
%
% The following formulas should be used to determine how to store
% the entry corresponding to row I and column J in the original matrix:
%
% Entries of A1:
%
% 1 <= I <= N1, 1 <= J <= N1, (J-I) <= MU and (I-J) <= ML.
%
% Store the I, J entry into location
% (I-J+MU+1)+(J-1)*(ML+MU+1).
%
% Entries of A2:
%
% 1 <= I <= N1, N1+1 <= J <= N1+N2.
%
% Store the I, J entry into location
% (ML+MU+1)*N1+(J-N1-1)*N1+I.
%
% Entries of A3:
%
% N1+1 <= I <= N1+N2, 1 <= J <= N1.
%
% Store the I, J entry into location
% (ML+MU+1)*N1+N1*N2+(J-1)*N2+(I-N1).
%
% Entries of A4:
%
% N1+1 <= I <= N1+N2, N1+1 <= J <= N1+N2
%
% Store the I, J entry into location
% (ML+MU+1)*N1+N1*N2+(J-1)*N2+(I-N1).
% (same formula used for A3).
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 03 March 2004
%
% Author:
%
% John Burkardt
%
% Parameters:
%
% Input, integer N1, N2, the order of the banded and dense blocks.
% N1 and N2 must be nonnegative, and at least one must be positive.
%
% Input, integer ML, MU, the lower and upper bandwidths.
% ML and MU must be nonnegative, and no greater than N1-1.
%
% Input, real A((ML+MU+1)*N1 + 2*N1*N2 + N2*N2), the R8CBB matrix.
%
% Input, integer I, J, the row and column of the entry to retrieve.
%
% Output, real VALUE, the value of the (I,J) entry.
%
%
% Check for I or J out of bounds.
%
if ( i <= 0 | n1+n2 < i )
fprintf ( 1, '\n' );
fprintf ( 1, 'R8CBB_GET - Fatal error!\n' );
fprintf ( 1, ' Illegal input value of row index I = %d\n', i );
error ( 'R8CBB_GET - Fatal error!' );
end
if ( j <= 0 | n1+n2 < j )
fprintf ( 1, '\n' );
fprintf ( 1, 'R8CBB_GET - Fatal error!\n' );
fprintf ( 1, ' Illegal input value of column index J = %d\n', j );
error ( 'R8CBB_GET - Fatal error!' );
end
%
% The A1 block of the matrix.
%
% Check for out of band problems.
%
if ( i <= n1 && j <= n1 )
if ( mu < (j-i) | ml < (i-j) )
value = 0.0;
return
else
ij = (i-j+mu+1)+(j-1)*(ml+mu+1);
end
%
% The A2 block of the matrix:
%
elseif ( i <= n1 && n1 < j )
ij = (ml+mu+1)*n1+(j-n1-1)*n1+i;
%
% The A3 and A4 blocks of the matrix.
%
elseif ( n1 < i )
ij = (ml+mu+1)*n1+n2*n1+(j-1)*n2+(i-n1);
end
value = a(ij);
return
end